The base of an equilateral triangle is along the line given by 3x+4y=9 . If a vertex of the triangle is 1,2  then the length of its side is

The perpendicular distance from vertex  1,2 to the base 3x+4y=9 is height h of the equilateral triangle h=31+41−932+42=25 If a  is the length of the side and h is height of an equilateral triangle then  a=2h3Therefore, the length of the side is a=453=0.4618